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on Game Theory |
| By: | Ben Amiet; Andrea Collevecchio; Marco Scarsini |
| Abstract: | Nash equilibria are a central concept in game theory and have applications in fields such as economics, evolutionary biology, theoretical computer science, and many others. Mixed equilibria exist in any finite game, but pure equilibria may fail to exist. We consider the existence of pure Nash equilibria in games where the payoffs are drawn at random. In particular, we consider games where a large number of players can each choose one of two possible actions, and the payoffs are i.i.d. with the possibility of ties. We provide asymptotic results about the random number of pure Nash equilibria, such as fast growth and a central limit theorem. Moreover, we establish a new link between percolation models and game theory to shed light on various aspects of Nash equilibria. Through this connection, we describe in detail the geometry of Nash equilibria and show that, when the probability of ties is small, a best-response dynamics reaches a Nash equilibrium with a probability that quickly approaches one as the number of players grows. We show a multitude of phase transitions depending on a single parameter of the model, that is, the probability of having ties. |
| Date: | 2019–05 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1905.10758&r=all |
| By: | Emma von Essen (Department of Economics and Business Economics, Aarhus University); Marieke Huysentruyt (Strategy and Business Policy, HEC Paris, and SITE, Stockholm School of Economics); Topi Miettinen (Department of Economics, Hanken School of Economics, Helsinki, and SITE, Stockholm School of Economics) |
| Abstract: | This paper analyzes a two-person, two-stage model of sequential exploration, where both information and payoff externalities exist, and tests the derived hypotheses in the laboratory. We theoretically show that even when agents are self-interested and perfectly rational, the information externality induces an encouragement effect: a positive effect of first-player exploration on the optimality of the second-player exploring as well. When agents have other-regarding preferences and imperfectly optimize, the encouragement effect is strongest. The explorative nature of the game raises the expected surplus compared to a payoff equivalent public goods game. We empirically confirm our main theoretical predictions using a novel experimental paradigm. Our findings are relevant for motivating and managing groups and teams innovating not only for private but also, and especially so, for public goods. |
| Keywords: | Economics: Behavior and Behavioral Decision Making, Economics: Game Theory and Bargaining Theory, Economics: Microeconomic Behavior, Industrial Organization: Firm Objectives, Organization and Behavior, Decision analysis: Sequential |
| JEL: | C72 C91 D03 D83 O31 |
| Date: | 2019–08–14 |
| URL: | http://d.repec.org/n?u=RePEc:aah:aarhec:2019-10&r=all |
| By: | Leininger, Wolfgang |
| Abstract: | The term "rent-dissipation" is prominently used in the theory of rent-seeking and its (game) theoretical vehicle contest theory. While in a pure strategy Nash equilibrium of a contest with finitely many players full rent-dissipation cannot occur, this is not the case if the same contests are analyzed with the solution concept of an evolutionarily stable strategy (ESS). Notably, even over-dissipation of a rent in pure strategy ESS is feasible! The paper explains these differences from a principle point of view by linking the ESS-solution theory in contests to the Nash equilibrium solution theory of transfer contests. This insight then not only makes the computation of the ESS-solution of a contest from the Nash solution of a transfer contest an easy exercise, but-more importantly - also leads to a reassessment of the ESS-"over-dissipation" results in the earlier literature: if one replaces the value of the rent with its transfer value, over-dissipation becomes incompatible with ESS, too. |
| Keywords: | contests,evolutionarily stable strategy,finite population,overdissipation |
| JEL: | C73 D72 D82 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:zbw:rwirep:809&r=all |
| By: | Claudia Cerrone (Max Planck Institute for Research on Collective Goods, Bonn); Francesco Feri (Royal Holloway, Department of Economics); Philip R. Neary (Royal Holloway, Department of Economics) |
| Abstract: | Existing models of regret aversion assume that individuals can make an ex-post comparison between their choice and a foregone alternative. Yet in many situations such a comparison can be made only if someone else chose the alternative option. We develop a model where regret-averse agents must decide between the status quo and a new risky option that outperforms the status quo in expectation, and learn the outcome of the risky option, if unchosen, with a probability that depends on the choices of others. This turns what was previously a series of single-person decision problems into a coordination game. Most notably, regret can facilitate coordination on the status quo { an action that would not be observed if the agents were acting in isolation or had standard preferences. We experimentally test the model and find that regret-averse agents behave as predicted by our theory. |
| Keywords: | regret aversion, coordination games, information |
| JEL: | C72 C92 D81 D91 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:mpg:wpaper:2019_10&r=all |
| By: | Ronald Stauber |
| Abstract: | The term “belief function” is generally used to refer to a class of capacities that can be viewed as representing ambiguity averse preferences. This paper introduces a definition of equilibrium for normal-form games with ambiguous beliefs, where belief functions are used to describe strategic uncertainty. To capture independence of strategies and beliefs, a novel notion of a “strategic product integral” is introduced for belief functions, based on the Möbius transform of a capacity, and shown to be different from the Choquet integral of an appropriate product capacity. A characterization of the integral in terms of maxmin expected utility expressed relative to elements of the cores of the respective belief functions, is also presented. The resulting equilibrium notion relies on the Möbius transform to embed objectively chosen probabilistic mixed strategies into ambiguous beliefs of opponents about these strategies, while incorporating stronger consistency requirements than those imposed by previous definitions of equilibria under ambiguity. Classification-C72, D81 |
| Keywords: | Belief functions; Product capacities; Equilibrium under ambiguity; Strategic uncertainty |
| Date: | 2019–04 |
| URL: | http://d.repec.org/n?u=RePEc:acb:cbeeco:2019-668&r=all |
| By: | Fu, Guanxing (HU Berlin); Horst, Ulrich (HU Berlin) |
| Abstract: | We analyze linear McKean-Vlasov forward-backward SDEs arising in leader-follower games with mean-field type control and terminal state constraints on the state process. We establish an existence and uniqueness of solutions result for such systems in time-weighted spaces as well as a (convergence) result of the solutions with respect to certain perturbations of the drivers of both the forward and the backward component. The general results are used to solve a novel single-player model of portfolio liquidation under market impact with expectations feedback as well as a novel Stackelberg game of optimal portfolio liquidation with asymmetrically informed players. |
| Keywords: | mean-field control; stackelberg game; mean-field game with a major player; McKean-Vlasov FBSDE; portfolio liquidation; singular terminal constraint; |
| Date: | 2019–07–30 |
| URL: | http://d.repec.org/n?u=RePEc:rco:dpaper:174&r=all |
| By: | Nils Bertschinger; Martin Hoefer; Daniel Schmand |
| Abstract: | In their seminal work on systemic risk in financial markets, Eisenberg and Noe proposed and studied a model with $n$ firms embedded into a network of debt relations. We analyze this model from a game-theoretic point of view. Every firm is a rational agent in a directed graph that has an incentive to allocate payments in order to clear as much of its debt as possible. Each edge is weighted and describes a liability between the firms. We consider several variants of the game that differ in the permissible payment strategies. We study the existence and computational complexity of pure Nash and strong equilibria, and we provide bounds on the (strong) prices of anarchy and stability for a natural notion of social welfare. Our results highlight the power of financial regulation -- if payments of insolvent firms can be centrally assigned, a socially optimal strong equilibrium can be found in polynomial time. In contrast, worst-case strong equilibria can be a factor of $\Omega(n)$ away from optimal, and, in general, computing a best response is an NP-hard problem. For less permissible sets of strategies, we show that pure equilibria might not exist, and deciding their existence as well as computing them if they exist constitute NP-hard problems. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.01714&r=all |
| By: | Espín, Antonio M.; Brañas-Garza, Pablo; Gamella, Juan; Herrmann, Benedikt; Martin, Jesus |
| Abstract: | Humans often punish non-cooperators in one-shot interactions among genetically-unrelated individuals. So-called altruistic punishment poses an evolutionary puzzle because it enforces a cooperation norm that benefits the whole group, but is costly for the punisher. Under the “big mistake” (or “mismatch”) hypothesis, social behavior such as punishment evolved by individual selection at a time when repeated interactions with kin prevailed. It then misfired in modern humans, who “mistakenly” apply it in sporadic interactions with unrelated individuals. In contrast, cultural group selection theories emphasize cultural differences in normative behavior and the role of intergroup competition and punishment for the emergence of large-scale cooperation in the absence of genetic relatedness. We conducted a series of multilateral-cooperation economic experiments with a sample of Spanish Romani people (Gitanos), who represent a unique cultural group to test the predictions of the two accounts: Gitano communities rely heavily on close kin-based networks, maintain high consanguinity rates and display a particularly strong sense of ethnic identity. A total of 320 Gitano and non-Gitano (i.e., the majority Spanish population) participants played a one-shot public goods game with punishment in either ethnically homogeneous or ethnically mixed (half Gitano and half non-Gitano) four-person groups. In the homogeneous groups, punishment was commonly used by non-Gitanos but virtually inexistent among Gitanos. In the mixed groups, however, Gitanos who did not cooperate were severely punished by other Gitanos, but also by non-Gitanos (particularly males in both cases). The results are more consistent with cultural group selection and also qualify some of its predictions. |
| Keywords: | cooperation, punishment, Gypsy/Roma, ethnicity, culture, evolution |
| JEL: | C93 H41 J71 Z13 |
| Date: | 2019–07–31 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95423&r=all |
| By: | Grund, Christian (RWTH Aachen University); Harbring, Christine (RWTH Aachen University); Thommes, Kirsten (University of Paderborn); Tilkes, Katja Rebecca (RWTH Aachen University) |
| Abstract: | We experimentally analyze whether the opportunity to receive a permanent contract motivates temporary group members in a public good setting and how this affects the other group members. We compare an exogenous and an endogenous decision mechanism to extend the temporary agent's group membership. The exogenous mechanism to extend the contract is modeled by a random draw. In the endogenous setting, one other group member decides about the temporary agent's future group membership. Our results reveal that both — the decision to extend a contract and the decision mechanism itself — affect not only the temporary group member's effort but also the efforts of the permanent group members and, ultimately, also cooperation within the group after the decision has been made. |
| Keywords: | cooperation, experiments, groups, public good games, teams, temporary employment |
| JEL: | C9 M5 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:iza:izadps:dp12513&r=all |
| By: | Armstrong, Mark; Vickers, John |
| Abstract: | We explore patterns of competitive interaction by studying mixed-strategy equilibrium pricing in oligopoly settings where consumers vary in the set of suppliers they consider for their purchase. In the case of "nested reach" we find equilibria, unlike those in existing models, in which price competition is segmented: small firms offer only low prices and large firms only offer high prices. We characterize equilibria in the three-firm case using correlation measures of competition between pairs of firms. We then contrast them with equilibria in the parallel model with capacity constraints. A theme of the analysis is how patterns of consumer consideration matter for competitive outcomes. |
| Keywords: | Bertrand-Edgeworth competition, price dispersion, consideration sets, mixed strategies, captive customers |
| JEL: | D43 D83 L11 L13 L15 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:pra:mprapa:95336&r=all |
| By: | Geoffroy de Clippel; Kfir Eliaz; Daniel Fershtman; Kareen Rozen |
| Abstract: | Each period, a principal must assign one of two agents to some task. Profit is stochastically higher when the agent is qualified for the task. The principal cannot observe qualification. Her only decision is which of the two agents to assign, if any, given the public history of selections and profits. She cannot commit to any rule. While she maximizes expected discounted profits, each agent maximizes his expected discounted selection probabilities. We fully characterize when the principal's first-best payoff is attainable in equilibrium, and identify a simple strategy profile achieving this first-best whenever feasible. We propose a new refinement for dynamic mechanisms (without transfers) where the designer is a player, under which we show the principal's next-best, when the first-best is unachievable, is the one-shot Nash. We show how our analysis extends to variations on the game accommodating more agents, caring about one's own performance, cheap talk and losses. |
| Keywords: | Dynamic allocation, mechanism design without transfers, mechanism design without commitment |
| JEL: | D82 D86 |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:bon:boncrc:crctr224_2019_116&r=all |
| By: | Morton, Alec; Arulselvan, Ashwin; Thomas, Ranjeeta |
| Abstract: | In recent years, donors such as the Bill and Melinda Gates Foundation have made an enormous contribution to the reduction of the global burden of disease. It has been argued that such donors should prioritise interventions based on their cost-effectiveness, that is to say, the ratio of costs to benefits. Against this, we argue that the donor should fund not the most cost-effective interventions, but rather interventions which are just cost-ineffective for the country, thus encouraging the country to contribute its own domestic resources to the fight against disease. We demonstrate that our proposed algorithm can be justified within the context of a model of the problem as a leader-follower game, in which a donor chooses to subsidise interventions which are implemented by a country. We argue that the decision rule we propose provides a basis for the allocation of aid money which is efficient, fair and sustainable. |
| Keywords: | Bilevel programming; Development aid; Game theory; Global health; Resource allocation; Stackelberg game |
| JEL: | N0 |
| Date: | 2018–03–01 |
| URL: | http://d.repec.org/n?u=RePEc:ehl:lserod:101210&r=all |
| By: | Ngo Van Long |
| Abstract: | How do economic agents manage expected shifts in regimes? How do they try to influence or prevent the arrival of such shifts? This paper provides a selective survey of the analysis of regime shifts from an economic view point, with particular emphasis on the use of the tech-niques of optimal control theory and differential games. The paper is organized as follows. Section 2 gives an overview of the concepts of regime shifts, thresholds, and tipping points. Section 3 shows how unknown tipping points affect the optimal current policy of decision makers, with or without ambiguity aversion. Section 4.s focus is on political regime shifts in a two-class economy: how the elite may try to prevent revolution by using policy instruments such as repression, redistribution, and gradual democratization. Section 5 reviews models of dynamic games in resource exploitation involving regime shifts and thresholds. Section 6 reviews some studies of regime shifts in industrial organization theory, with focus on R&D races, including efforts to sabotage rivals in order to prevent entry. Section 7 reviews games of regime shifts when players can manage a Big Push. Section 8 discusses some directions for future research. |
| Keywords: | regime shifts, thresholds, tipping points, political repression, democratization |
| JEL: | C00 C70 |
| Date: | 2019 |
| URL: | http://d.repec.org/n?u=RePEc:ces:ceswps:_7749&r=all |
| By: | Simina Br\^anzei; Yuval Peres |
| Abstract: | The stochastic multi-armed bandit problem is a classic model illustrating the tradeoff between exploration and exploitation. We study the effects of competition and cooperation on this tradeoff. Suppose there are $k$ arms and two players, Alice and Bob. In every round, each player pulls an arm, receives the resulting reward, and observes the choice of the other player but not their reward. Alice's utility is $\Gamma_A + \lambda \Gamma_B$ (and similarly for Bob), where $\Gamma_A$ is Alice's total reward and $\lambda \in [-1,1]$ is a cooperation parameter. At $\lambda = -1$ the players are competing in a zero-sum game, at $\lambda = 1$, they are fully cooperating, and at $\lambda = 0$, they are neutral: each player's utility is their own reward. The model is related to the economics literature on strategic experimentation, where usually the players observe each other's rewards. In the discounted setting, the Gittins index reduces the one-player problem to the comparison between a risky arm, with a prior $\mu$, and a predictable arm with success probability $p$. The value of $p$ where the player is indifferent between the arms is the Gittins index $g(\mu,\beta) > m$, where $m$ is the mean of the risky arm and $\beta$ the discount factor. We show that competing players explore less than a single player: there is $p^* \in (m, g(\mu, \beta))$ so that for all $p > p^*$, the players stay at the predictable arm. However, the players are not completely myopic: they still explore for some $p > m$. On the other hand, cooperating players explore more than a single player. Finally, we show that neutral players learn from each other, receiving strictly higher total rewards than they would playing alone, for all $ p\in (p^*, g(\mu,\beta))$, where $p^*$ is the threshold above which competing players do not explore. We show similar phenomena in the finite horizon setting. |
| Date: | 2019–08 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1908.01135&r=all |
| By: | Kim, Miseok; Kim, So-Jin; Yoo, Do-il |
| Keywords: | Agribusiness |
| Date: | 2019–06–25 |
| URL: | http://d.repec.org/n?u=RePEc:ags:aaea19:290712&r=all |
| By: | Vasudha Jain; Mark Whitmeyer |
| Abstract: | Firms strategically disclose product information in order to attract consumers, but recipients often find it costly to process all of it, especially when products have complex features. We study a model of competitive information disclosure by two senders, in which the receiver may garble each sender's experiment, subject to a cost increasing in the informativeness of the garbling. As long as attention costs are not too low, there is an interval of prior means over which it is an equilibrium for both senders to offer full information, which interval expands as attention costs grow. Information on one sender substitutes for information on the other, which allows the receiver to nullify the profitability of a deviation. We thus provide a novel channel through which competition encourages information disclosure. |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:arx:papers:1907.09255&r=all |
| By: | Bracke, Philippe (UK Financial Conduct Authority); Datta, Anupam (Carnegie Mellon University); Jung, Carsten (Bank of England); Sen, Shayak (Carnegie Mellon University) |
| Abstract: | We propose a framework for addressing the ‘black box’ problem present in some Machine Learning (ML) applications. We implement our approach by using the Quantitative Input Influence (QII) method of Datta et al (2016) in a real‑world example: a ML model to predict mortgage defaults. This method investigates the inputs and outputs of the model, but not its inner workings. It measures feature influences by intervening on inputs and estimating their Shapley values, representing the features’ average marginal contributions over all possible feature combinations. This method estimates key drivers of mortgage defaults such as the loan‑to‑value ratio and current interest rate, which are in line with the findings of the economics and finance literature. However, given the non‑linearity of ML model, explanations vary significantly for different groups of loans. We use clustering methods to arrive at groups of explanations for different areas of the input space. Finally, we conduct simulations on data that the model has not been trained or tested on. Our main contribution is to develop a systematic analytical framework that could be used for approaching explainability questions in real world financial applications. We conclude though that notable model uncertainties do remain which stakeholders ought to be aware of. |
| Keywords: | Machine learning; explainability; mortgage defaults |
| JEL: | G21 |
| Date: | 2019–08–09 |
| URL: | http://d.repec.org/n?u=RePEc:boe:boeewp:0816&r=all |
| By: | Julio A. Carrillo (Banco de México (E-mail: jcarrillo@banxico.org.mx)); Enrique G. Mendoza (University of Pennsylvania (E-mail: egme@sas.upenn.edu)); Victoria Nuguer (Inter-American Development Bank (E-mail: victorian@iadb.org)); Jessica Roldán-Peña (Banco de México (E-mail: jroldan@banxico.org.mx)) |
| Abstract: | Violations of Tinbergen's Rule and strategic interaction undermine monetary and financial policies significantly in a New Keynesian model with the Bernanke-Gertler accelerator. Welfare costs of risk shocks are large because of efficiency losses and income effects of costly monitoring, but they are larger under a simple Taylor rule (STR) and a Taylor rule augmented with credit spreads (ATR) than under a dual rules regime (DRR) with a Taylor rule and a financial rule targeting spreads, by 264 and 138 basis points respectively. ATR and STR are tight money-tight credit regimes that respond too much to inflation and not enough to spreads, and yield larger fluctuations in response to risk shocks. Reaction curves display shifts from strategic substitutes to complements in the choice of policy-rule elasticities. The Nash equilibrium is also a tight money-tight credit regime, with welfare 30 basis points lower than in Cooperative equilibria and the DRR, but still sharply higher than in the ATR and STR regimes. |
| Keywords: | Monetary policy, Financial frictions, Macroprudential policy, Leaning against the wind, Policy coordination |
| JEL: | E3 E44 E52 G18 |
| Date: | 2019–07 |
| URL: | http://d.repec.org/n?u=RePEc:ime:imedps:19-e-08&r=all |